Graphing Quadratics Lesson (5.1),(5.2)

8/8/2019 Graphing Quadratics Lesson (5.1),(5.2)

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Linear Functions

How to Graph using Slope, Y-int, X-int, Table,

Graphing Calc

How to Write Linear Equations

How to Graph Linear Inequalities


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QUADRATIC FUNCTIONS


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GRAPHING A QUADRATIC FUNCTION

A quadratic function has the form

y =ax2 +bx+c where a { 0.


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The graph is U-shaped and is called

a parabola.


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The highest or lowest point on the

parabola is called the vertex.


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In general, the axis of symmetry for

the parabola is the vertical line

through the vertex.


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These are the graphs of y =x2

and y =x2.


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The origin is the vertex for both

graphs.

The origin is the lowest point on the

graph of y =x2, and the highest point

on the graph of y =x2

.


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They-axis is the axis of symmetry

for both graphs.


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THE GRAPH OF A QUADRATIC FUNCTION


CONCEPT

SUMMARY

The y-intercept is at (0, c).

The graph of y = ax2

+ bx + c is a parabola with these characteristics:

The parabola opens up ifa > 0 and opens down ifa < 0.The parabola is wider than the graph of y = x

2if a < 1 and

narrower than the graph y = x2

if a > 1.


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Graph y = 2x2 8x+ 6

SOLUTION

Note The y-intercept is (0, 6)

Since a >0, the parabola opens up.

Graphing a Quadratic Function

x y

-1 160 6

1 0

x y

2 -23 0

4 6

(0, 6)

(2,2)


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(2,2)

Graphing a Quadratic Function

Graphgiven Vertex (2, -2) and y-intercept 6

Draw a parabola through the plottedpoints.

(0, 6) (4, 6)Plot the vertex.

Plot the y-intercept (0, 6) and its

symmetric point, (4, 6).

Draw the axis of symmetry x=2.


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Finding the Vertex on TI83 if the

Parabola Opens Down Step 1: Graph the function

Step2: Press 2nd (yellow

button), CALC (above the

blue menu button TRACE)

Step 3: Select 4:

maximum. Press

ENTER. You will be back

at the graph screen.


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Parabola Opens Down Step4: You will be back at

the graph screen and will be

prompted for a left

bound. Move the cursor to apoint to the left of the

vertex. Then press ENTER.

Step 5: You will now be

prompted for a right

bound. Move the cursor to a

point to the right of the

vertex. Then press ENTER


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Parabola Opens Down

Step6: You will be

prompted to guess where the

vertex is. Move the cursor to

a point as close as possible tothe vertex. Then press

ENTER.

Step 7: The answer will be

displayed at the bottom of

the screen. In this example,

the answer is (1.71, 542.86).

Graphing Quadratics Lesson (5.1),(5.2)

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